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arXiv · 2603.20979

Second-Order Bi-Scalar-Vector-Tensor Field Equations Compatible with Conservation of Charge in a Space of Four-Dimensions

Gregory W. Horndeski
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Abstract

The purpose of this paper is to explore, in a space of four-dimensions, the possible forms that second-order, bi-scalar-vector-tensor field equations derivable from a variational principle can assume. In order to restrict this enormous class of field equations I shall first require that the equations governing the vector field (which will be identified with the vector potential of an electromagnetic field) be consistent with the notion of conservation of charge. Secondly I shall require that these vector equations reduce to Maxwell's equations in a flat space when the scalar fields are constant. Unfortunately even with these two powerful restrictions on the form of the field equations I have not been able to construct a Lagrangian which yields all possible field equations of this nature. This situation will lead to a discussion of other ways in which the field equations can be restricted to obtain viable bi-scalar-vector-tensor field equations. Lastly I shall make a few remarks on how the results obtained can be used to show that the Higgs field can generate electromagnetic fields in the early Universe, and how to couple bi-scalar fields to gauge-tensor fields to construct second-order, bi-scalar-Yang-Mills-tensor field theories compatible with the conservation of gauge charge.

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Gregory W. Horndeski. 2026-04-20. Second-Order Bi-Scalar-Vector-Tensor Field Equations Compatible with Conservation of Charge in a Space of Four-Dimensions. https://arxiv.org/abs/2603.20979

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